Q1 of 40 Page 92

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save D2000 per month, find their monthly income.

Let the monthly incomes be represented by x and their expenditure be represented by y.

According to the given income ratios,


Income of the first person is 9x and that of the second persons is 7x.


According to the given expenditure ratios;


Expenditure of the first person is 4y and the second person’s is 3y.


Both of them manage to save ₹2000 per month.


i.e. income – expenditure = savings


Then,


9x – 4y = 2000 …I


7x - 3y = 2000 …II


Multiplying I by 3 and II by 4, we get


27x – 12y = 6000 …III


28x – 12y = 8000 …IV


Subtracting III from IV, we get


x = 2000


Putting x = 2000 in I we get,


18000 – 4y = 2000


⇒ 16000 = 4y


⇒ y = 4000


Now,


Income of the first person = 9x = 9× 2000 = 18000


Income of the second person = 7x = 7× 2000 = 14000


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